Suppose . What is the smallest possible value for ?

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Suppose $\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$ . What is the smallest possible value for $x$ ?

AWESOMEEE May 25, 2015

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Best Answer

+129852

+10

1/2 + 1/3 +......+ 1/x > 3/2

5/6 + 1/4 + 1/5 +.......+ 1/x > 3/2

1/4 + 1/5 +......+ 1/x > 2/3

9/20 + 1/6 + 1/7 > 2/3

1/6 + 1/7 > 13/60

1/7 > 1/20

So.....7 is the smallest integer

CPhill May 25, 2015

1⁺⁰ Answers

+129852

+10

Best Answer

1/2 + 1/3 +......+ 1/x > 3/2

5/6 + 1/4 + 1/5 +.......+ 1/x > 3/2

1/4 + 1/5 +......+ 1/x > 2/3

9/20 + 1/6 + 1/7 > 2/3

1/6 + 1/7 > 13/60

1/7 > 1/20

So.....7 is the smallest integer

CPhill May 25, 2015

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